Ramsey’s theorem and products in the Weihrauch degrees

Dzhafarov, Damir D.; Goh, Jun Le; Hirschfeldt, Denis R.; Patey, Ludovic; Pauly, Arno

doi:10.3233/com-180203

Journal article 919 views 184 downloads

Ramsey’s theorem and products in the Weihrauch degrees

Damir D. Dzhafarov, Jun Le Goh, Denis R. Hirschfeldt, Ludovic Patey, Arno Pauly

Computability, Volume: 9, Issue: 2, Pages: 85 - 110

Swansea University Author: Arno Pauly

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DOI (Published version): 10.3233/com-180203

Abstract

We study the positions in the Weihrauch lattice of parallel products of various combinatorial principles related to Ramsey’s theorem. Among other results, we obtain an answer to a question of Brattka, by showing that Ramsey’s theorem for pairs (RT22) is Weihrauch-incomparable to the parallel product...

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Published in:	Computability
ISSN:	2211-3568 2211-3576
Published:	IOS Press 2020
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa53985

first_indexed	2020-05-15T13:07:22Z
last_indexed	2023-01-11T14:31:49Z
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spelling	2022-12-05T12:42:32.0959742 v2 53985 2020-04-18 Ramsey’s theorem and products in the Weihrauch degrees 17a56a78ec04e7fc47b7fe18394d7245 0000-0002-0173-3295 Arno Pauly Arno Pauly true false 2020-04-18 MACS We study the positions in the Weihrauch lattice of parallel products of various combinatorial principles related to Ramsey’s theorem. Among other results, we obtain an answer to a question of Brattka, by showing that Ramsey’s theorem for pairs (RT22) is Weihrauch-incomparable to the parallel product of the stable Ramsey’s theorem for pairs and the cohesive principle (SRT22×COH). Journal Article Computability 9 2 85 110 IOS Press 2211-3568 2211-3576 Computable combinatorics, Ramsey theory, computability theory, reverse mathematics 13 5 2020 2020-05-13 10.3233/com-180203 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2022-12-05T12:42:32.0959742 2020-04-18T18:48:54.8790381 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Damir D. Dzhafarov 1 Jun Le Goh 2 Denis R. Hirschfeldt 3 Ludovic Patey 4 Arno Pauly 0000-0002-0173-3295 5 53985__17093__46c35448f6164a72ad603fffb6c282b2.pdf Products_420.pdf 2020-04-18T18:50:39.0486068 Output 888875 application/pdf Accepted Manuscript true true eng
title	Ramsey’s theorem and products in the Weihrauch degrees
spellingShingle	Ramsey’s theorem and products in the Weihrauch degrees Arno Pauly
title_short	Ramsey’s theorem and products in the Weihrauch degrees
title_full	Ramsey’s theorem and products in the Weihrauch degrees
title_fullStr	Ramsey’s theorem and products in the Weihrauch degrees
title_full_unstemmed	Ramsey’s theorem and products in the Weihrauch degrees
title_sort	Ramsey’s theorem and products in the Weihrauch degrees
author_id_str_mv	17a56a78ec04e7fc47b7fe18394d7245
author_id_fullname_str_mv	17a56a78ec04e7fc47b7fe18394d7245_***_Arno Pauly
author	Arno Pauly
author2	Damir D. Dzhafarov Jun Le Goh Denis R. Hirschfeldt Ludovic Patey Arno Pauly
format	Journal article
container_title	Computability
container_volume	9
container_issue	2
container_start_page	85
publishDate	2020
institution	Swansea University
issn	2211-3568 2211-3576
doi_str_mv	10.3233/com-180203
publisher	IOS Press
college_str	Faculty of Science and Engineering
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department_str	School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
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description	We study the positions in the Weihrauch lattice of parallel products of various combinatorial principles related to Ramsey’s theorem. Among other results, we obtain an answer to a question of Brattka, by showing that Ramsey’s theorem for pairs (RT22) is Weihrauch-incomparable to the parallel product of the stable Ramsey’s theorem for pairs and the cohesive principle (SRT22×COH).
published_date	2020-05-13T02:08:48Z
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Ramsey’s theorem and products in the Weihrauch degrees

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